Various probabilistic models have been developed to handle data that comprises of both continuous and discrete features.
Ramchandran et al. [1]} extended the GPLVM to handle multiple likelihoods with a sampling-based variational inference technique.
Their work enables heterogeneous datasets to be represented with low dimensional embeddings.
Valera et al. [2]} proposed a general Bayesian non-parametric latent variable model for heterogeneous datasets.
Several authors ([3]}, [4]}, [5]}) have introduced VAE-based methods for handling heterogeneous and incomplete data with various likelihood models.
Nazabel et al. [4]} proposed a model that enables the sharing of network parameters among different attributes for a single sample. Antelmi et al. [3]} proposed a multi-channel approach, where each channel (each with a different likelihood) shares a common target prior on the latent representation. Ma et al. [5]} trained individual marginal VAEs for every single variable to obtain the latent encoding for each variable and then fed them to a new multi-dimensional VAE.
However, these models cannot capture any correlations among different samples.
Although the models mentioned so far have not been designed for time-series or longitudinal datasets, methods that explore the domain of time-series data include, for example, the work of [9]} that extends multi-output regression model for heterogeneous data.
The approach by Gootjes et al. [10]} enables longitudinal data modelling for heterogeneous datasets.
They proposed a modular Bayesian network over the latent presentations of grouped variables obtained from HI-VAE so that each group of variables can be heterogeneous.
However, their model requires a careful design of possible graph structures.
